Sample paper · GCSE Higher · grades 4–9
GCSE Higher sample Paper 2 (calculator)
The real Paper 2 is 1.5 hour 30 minutes and 80 marks, calculator, and all three papers carry equal weight. This sample is 20 original questions in the same content proportions as the Higher qualification — number 15%, algebra 30%, ratio, proportion and rates of change 20%, geometry and measures 20%, probability 7.5%, statistics 7.5% — with a calculator allowed. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.
CalculatorGCSE Higher
GCSE Higher sample Paper 2 (calculator)
MathsUKwww.geekhero.co.uk
- 1.Work out the value of .
- 2.Solve 2x² − 7x + 3 = 0.
- 3.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.
- 4.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?
- 5.A fair coin is flipped and a fair five-sided spinner, labelled 1 to 5, is spun. All the outcomes are listed as pairs, such as (H, 3). Work out the probability that the outcome is a tail and an odd number.
- 6.Priya travels to work by one of two routes and records her journey times, in minutes, over several weeks. Route 1 has a median of 34 minutes and an interquartile range of 22 minutes. Route 2 has a median of 41 minutes and an interquartile range of 6 minutes. Priya wants the more reliable route for getting to an important meeting on time. Which route should she choose, and why?
- 7.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.
- 8.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.
- 9.A factory machine produces bottles at a constant rate. In 45 minutes it produces 810 bottles. The factory needs 2,160 bottles for an order. Working at the same rate, work out how many minutes it will take to produce the order.
- 10.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.
- 11.A two-way table records how 180 students at a school travel: by bus or on foot, split by year group. There are 84 students in Year 11, of whom 38 travel by bus and the rest walk. The rest of the 180 students are in Year 10, and 42 of the Year 10 students travel by bus. Work out the probability that a randomly chosen Year 10 student walks to school. Give your answer as a fraction in its simplest form.
- 12.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.
- 13.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.
- 14.A 1.5 kg bag of pasta costs £2.85 and a 2.4 kg bag of the same pasta costs £4.32. Work out which bag gives better value for money.
- 15.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?
- 16.y = 5 − 2x. Work out the value of x when y = 11.
- 17.On a straight-line graph the volume of water, V litres, in a tank is plotted on the vertical axis and the time, t minutes, on the horizontal axis. The line passes through (2, 50) and (6, 130). Work out the gradient of the line and give its units.
- 18.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.
- 19.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.
- 20.A candidate solves the inequality x² > 9 and writes: "x² > 9, so x > 3." Which of these is a correct comment on the candidate's work?
How the 20 questions are shared out
- Number — 3 questions (15% of the qualification)
- Algebra — 6 questions (30% of the qualification)
- Ratio, proportion and rates of change — 4 questions (20% of the qualification)
- Geometry and measures — 4 questions (20% of the qualification)
- Probability — 2 questions (7.5% of the qualification)
- Statistics — 1 question (7.5% of the qualification)
Where an area has fewer printable questions than its share, the shortfall is filled from the other areas. These are original questions, not past papers.